Std 6 Mathematics · Chapter 11

11. Decimal Fractions

Solutions to Practice Set 11.1, Practice Set 11.2 and Exercise 11. Maharashtra State Board (Balbharati), Grade Six Mathematics.

About the chapter

Fractions with denominator 10, 100 or 1000 can be written as decimal fractions. In this chapter, we learn the place value of digits after the decimal point. We compare decimal fractions and write them in order. We also add and subtract decimal fractions.

Key points

The digits after the decimal point are in the tenths, hundredths and thousandths places.
The number of zeros in the denominator tells the number of digits after the decimal point.
Writing zeros at the end of a decimal fraction does not change its value. 0.8 = 0.80
To compare decimals, first compare the integer parts. Then compare tenths, hundredths and so on.
While adding or subtracting, write the decimal points one below the other.

Formulas and terms

Integer part – the part to the left of the decimal point. In 15.9, it is 15.
Tenths place – 1/10 = 0.1
Hundredths place – 1/100 = 0.01
Thousandths place – 1/1000 = 0.001

Practice Set 11.1

1Write the following fractions as decimal fractions.

(i) 16/100 = 0.16
(ii) 275/1000 = 0.275
(iii) 6/100 = 0.06
(iv) 269/100 = 2.69
(v) 15/1000 = 0.015
(vi) 235/10 = 23.5
(vii) 7/1000 = 0.007
(viii) 6 3/10 = 6.3

2Write the place value of the underlined digits.

(i) 34.26 – 2 is in the tenths place. Place value = 0.2
(ii) 8.88 – 8 is in the hundredths place. Place value = 0.08
(iii) 0.81 – 1 is in the hundredths place. Place value = 0.01
(iv) 0.40 – 4 is in the tenths place. Place value = 0.4
(v) 6.64 – 6 is in the units place. Place value = 6

3Determine the smaller and the larger number.

(i) 0.2, 0.4 – Smaller 0.2, larger 0.4
(ii) 70.08, 70.4 – Smaller 70.08, larger 70.4
(iii) 6.6, 6.58 – Smaller 6.58, larger 6.6
(iv) 7.4, 7.35 – Smaller 7.35, larger 7.4
(v) 0.76, 0.8 – Smaller 0.76, larger 0.8

Tip: Make the decimal places equal by writing zeros at the end. 6.6 = 6.60 and 0.8 = 0.80

4Write the following numbers in ascending and descending order.

(i) 8.6, 8.59, 8.09, 8.8

Ascending order : 8.09, 8.59, 8.6, 8.8
Descending order : 8.8, 8.6, 8.59, 8.09

(ii) 7.8, 7.66, 8.06, 8.68

Ascending order : 7.66, 7.8, 8.06, 8.68
Descending order : 8.68, 8.06, 7.8, 7.66

Practice Set 11.2

1Add the following numbers.

(i) 24.11 + 3.80 = 27.91
(ii) 14.01 + 1.10 + 1.98 = 17.09
(iii) 8.85 + 0.51 = 9.36
(iv) 2.30 + 18.84 = 21.14

2Subtract the following numbers.

(i) 0.86 − 0.34 = 0.52
(ii) 1.75 − 0.41 = 1.34
(iii) 6.42 − 3.30 = 3.12
(iv) 1.7 − 0.9 = 0.8
(v) 4.0 − 1.7 = 2.3
(vi) 7.63 − 4.00 = 3.63

3Write as a common fraction, improper fraction or mixed fraction.

(i) 0.9 = 9/10
(ii) 0.07 = 7/100
(iii) 0.191 = 191/1000
(iv) 0.049 = 49/1000
(v) 4.36 = 436/100 = 109/25 = 4 9/25
(vi) 0.015 = 15/1000 = 3/200
(vii) 4.56 = 456/100 = 114/25 = 4 14/25
(viii) 5.84 = 584/100 = 146/25 = 5 21/25

Exercise 11

1Fill in the blanks.

(i) The fraction 0.8 is written as a common fraction as 8/10.
(ii) The integer part of the number 15.9 is 15.
(iii) The digit in the ten's place in 171.9 is 7.
(iv) The place value of 8 in 9.8 is 0.8.
(v) The place value of 5 in 33.52 is 0.5.

2Write the decimal fractions as common fractions and reduce them to simplest form.

(i) 0.2 = 2/10 = 1/5
(ii) 0.62 = 62/100 = 31/50
(iii) 0.605 = 605/1000 = 121/200
(iv) 0.017 = 17/1000
(v) 5.46 = 546/100 = 273/50 = 5 23/50

3Solve.

(i) 23.84 + 12.37 = 36.21
(ii) 5.617 + 4.594 = 10.211
(iii) 12.78 + 10.25 = 23.03
(iv) 61.7 − 45.2 = 16.5
(v) 9.47 − 6.82 = 2.65
(vi) 17.93 − 15.82 = 2.11

4Write the place value of each digit in the number 246.135.

2 – hundreds place – 200
4 – tens place – 40
6 – units place – 6
1 – tenths place – 0.1
3 – hundredths place – 0.03
5 – thousandths place – 0.005

5Anita runs 3.27 km every morning and 2.8 km in the evening. How many kilometres does she run in a day?

Distance run in the morning = 3.27 km
Distance run in the evening = 2.80 km
Total distance = 3.27 + 2.80 = 6.07 km

Anita runs 6.07 km in a day.

← 10. Magical Mathematics – 1 All Std 6 Maths chapters →